A dwarf fortress can already very much be dungeon-like when abandoned. However I think it would be fun to have a mode specifically around the idea of creating a dungeon. You'd control the servants and slaves of a "dark lord" type character. Could be an evil human warlord, a dark wizard when they appear in the game, a demon, or an intelligent megabeast (I'm not sure if they are? Dragons maybe?). These servants/slaves could be of many races, even humans, elves and dwarves in addition to the more obvious goblins and kobolds. You could even command demons and other powerful evil creatures once you get you're dungeon established enough. There'd be nobles of a sort, almost certainly including the Dungeon Master. If you get you're dungeon to a high enough level you could even get the dark lord himself, or one of his lieutenants, similar to the way the dwarven monarch can choose to live at you're fortress.
The dungeon would have wealth like a fortress, but also a "danger" stat. Increasing danger makes you're dark lord happy and he might send some gifts. There'd be a caravan of sorts as well, as well as perhaps the goblin caravan. In addition wealth and danger will attract adventurers that seek to take you're wealth and/or defeat the danger that the dungeon presents to the surrounding countryside. If you're danger is high enough you might even get attacked by an army! Once the Army Arc is underway (which is actually probably going to be long before this idea is implemented if it ever is), you could send out raiders. Doing this increases danger and can of course be a source of loot for the dungeon.